Question

In the roll of two dice, what total number is the most likely to occur? Is there an energy reason why this number is favoured? Would energy have to be spent to increase the probability of getting a particular number (that is, to cheat)?

Short answer

The total number is themost likely to occur is 7.The reason behind thetotal number 7is most likely to occur due to probability as more combinations are present.Yes energy has to be spent to increase the probabilityof getting a particular number.

Step-by-step solution

Step 1: Introduction to the Concept

The probability is calculated using the following mathematical formula:

$\mathit{P}\mathbf{=}\frac{\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{f}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{u}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}}{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{p}\mathbf{o}\mathbf{s}\mathbf{s}\mathbf{i}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}}$

Positional probabilityis a sort of probability that is based on the number of arrangements in space that result in a certain condition.

Step 2: Explanation of total number is most likely to occur

The table below depicts the probable outcomes when two dice are rolled:

Dice1	1	2	3	4	5	6
Dice 2
1	2	3	4	5	6	7
2	3	4	5	6	7	8
3	4	5	6	7	8	9
4	5	6	7	8	9	10
5	6	7	8	9	10	11
6	7	8	9	10	11	12

In the table above, adding these numbers yields the total of two dice. The overall number of conceivable configurations is seven, with six of them being the most frequent.

Expected value $of x=P\left(x\right)$

$$\begin{gathered} =2\times \frac{1}{36}+3\times \frac{2}{36}+4\times \frac{3}{36}+5\times \frac{4}{36}+6\times \frac{5}{36}+7\times \frac{6}{36}+8\times \frac{5}{36}+9\times \frac{4}{36} \\ +10\times \frac{3}{36}+11\times \frac{2}{36}+12\times \frac{1}{36} \end{gathered}$$

role="math" localid="1658743844729" $=\frac{252}{36}$

$=7$

The reason for the total number that is most likely to occur being 7 is due to probability, since there are more combinations that result in a total of 7.

Sum$=\frac{1+2+3+4+5+6}{6}$

$=3.5$

Step 3: Explanation for getting a particular number

As a result, the sum of two dice must equal twice the sum of one die, which equals 7.

The probability of receiving number 7 is higher than that of other numbers which is $\frac{6}{36}$ .Work would now have to be done to change the system's inherent probability.

As a result, energy is required to enhance the probability of receiving a particular number.